Season the Chicken
Season both sides of the chicken breasts with salt, pepper, garlic powder, and thyme. Set aside.
Caramelize the Onions
In a large oven-safe skillet, heat 1 tablespoon of olive oil over medium heat. Add the sliced onions and cook, stirring occasionally, for about 20-25 minutes or until they are golden brown and caramelized. If desired, add balsamic vinegar during the last few minutes to enhance the flavor. Remove the onions from the skillet and set aside.
Sear the Chicken
Add the remaining tablespoon of olive oil to the skillet. Place the seasoned chicken breasts in the skillet and cook for about 5 minutes per side, or until golden brown. Remove the chicken and set aside.
Prepare the Sauce
Return the caramelized onions to the skillet and add the beef broth, thyme, and rosemary. Stir and bring to a simmer. Allow the sauce to reduce slightly, about 5 minutes.
Combine and Top with Cheese
Place the chicken back in the skillet, nestling it into the onions and sauce. Top each piece of chicken with a generous amount of shredded Gruyère or Swiss cheese.
Broil (Optional)
Transfer the skillet to the oven and broil for 2-3 minutes, or until the cheese is melted and bubbly. Watch closely to avoid burning.
Serve
Garnish with fresh parsley and serve hot with crusty bread, mashed potatoes, or a side salad.